mcmc

A Rust library implementing various MCMC diagnostics and utilities, such as Gelman Rubin potential scale reduction factor (R hat), effective sample size (ESS), chain splitting, and others.

This crate is language agnostic and intended to work with the outputs of any MCMC sampler (e.g. Stan, PyMC3, Turing.jl, etc).

Implementation

Currently we expect plain vectors of f64 floating point numbers, but this may be worth generalizing to f32s as well (see roadmap below).

Implementations for some of these diagnostics vary slightly, so reference implementations are based on Stan, and unit tests are adapted from the Stan codebase to ensure matching behavior.

Roadmap

Diagnostics

• Potential scale reduction factor
• Split potential scale reduction factor
• Effective sample size
• Monte Carlo Standard Error

Utilities

• Split chains as recommended in Vehtari, et al 2019
• Thinning

Data structures

• Introduce Num type to generalize our implementations to work for f32 or f64.
• Would it be helpful to have some kind of struct that can represent one or more sample chains with a parameter name?

Performance

• Remove unnecessary copying or allocation

References

[1]: Stephen P. Brooks and Andrew Gelman. General Methods for Monitoring Convergence of Iterative Simulations. Journal of Computational and Graphical Statistics, 7(4), 1998.

[2]: Andrew Gelman and Donald B. Rubin. Inference from Iterative Simulation Using Multiple Sequences. Statistical Science, 7(4):457-472, 1992.

[3]: Aki Vehtari, Andrew Gelman, Daniel Simpson, Bob Carpenter, Paul-Christian Burkner. Rank-normalization, folding, and localization: An improved R-hat for assessing convergence of MCMC, 2019. Retrieved from http://arxiv.org/abs/1903.08008.

[4]: Geyer, Charles J. Introduction to Markov Chain Monte Carlo. Handbook of Markov Chain Monte Carlo, edited by Steve Brooks, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng. Chapman; Hall/CRC. 2011.

Acknowledgements

Thanks to Ivan Ukhov for generously providing the mcmc namespace on Cargo.